| Abstract: |
| The bichromatic control of trapped-ion quantum states is a rich, bilinear control problem that has yielded important results on infinite-dimensional controllability\cite{BBR_ITAC2010}. Under specific experimental conditions, it is possible to truncate the space to be a finite-dimensional state space~\cite{RanganPRL2004}, controllable by two control matrices, albeit one where one of the two is real, and the other is imaginary~\cite{RanganJMP2005}. In this work, we examine a popular adiabatic control process, namely STIRAP~\cite{OregPRA1984}, in the context of this Hamiltonian, and explore the geometric aspects of control. We investigate if the STIRAP control of trapped-ion quantum states can be interpreted as steering the system through eigenvalue intersections.
\bibitem{BBR_ITAC2010} A.M. Bloch, R.W. Brockett, and C. Rangan, 2010, Finite Controllability of Infinite-Dimensional Quantum Systems, IEEE Transactions on Automatic Control, v. 55, pp.1797-1805.
\bibitem{RanganPRL2004} C.Rangan, A.M. Bloch, C. Monroe, and P.H. Bucksbaum, Physical Review Letters {\bf 92}, 113004 (2004).
\bibitem{RanganJMP2005} C.Rangan and A. M. Bloch, Journal of Mathematical Physics {\bf 46}, 032106 (2005).
\bibitem{OregPRA1984} J. Oreg, F.T. Hioe and J.H. Eberly, Phys. Rev. A {\bf 29}, 690 (1984). |
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